Open University

Tampere

Analysis A: Limit and Continuity, Small group teaching

<p>Email: <span class="spamspan"><span class="u">open.studies.tau</span> [at] <span class="d">tuni.fi</span><span class="t"> (open[dot]studies[dot]tau[at]tuni[dot]fi)</span></span><br>Phone: 0294 520 881</p><p>More information concerning Open University studies<br><a href="https://www.tuni.fi/open-university">tuni.fi/open-university</a></p>

Intermediate studies

Faculty of Information Technology and Communication Sciences

Technology and Natural Sciences

<p>Apply for Open University studies by using the following links:</p><p><ul><li><a href="https://tau-avoin.ilmoittaudu.fi/lobby/?realization=J-otm-f0104c34-21b9-44ba-8497-3f63352e4d6e-tampere-MATHMA420" target="_blank">MATH.MA.420 Analysis A: Limit and Continuity, small group teaching, Tampere</a></li></ul></p><p>You can find a link to the Open University Admissions service and application instructions on the <a href="https://www.tuni.fi/en/study-with-us/open-higher-education-studies/open-university/applying-open-university">Applying to Open University studies</a> page.</p><p>Some of the studies require prior studies. For example, studying intermediate studies may require some completed basic studies. These are described on the Information about studies tab of the study unit under prior requirements.</p><p>When you have been admitted to the studies, you must enrol separately via the Sisu information system for the implementation of the unit of study and, for example if set, for a practise group of your choice. You will receive instructions on how to do this by e-mail after you have confirmed your acceptance of the study place by paying the required fee.</p>

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Hervanta Campus

Contact teaching

<p>Look information at <a href="https://www.tuni.fi/en/study-with-us/open-higher-education-studies/open-university/applying-open-university">Applying to Open University studies</a>.</p>

<p>Real numbers, the least upper bound and the greatest lower bound, the limit of a sequence, Bolzano-Weierstrass Theorem, the limit of a function and the epsilon-delta proofs, continuity of a function,&#160;Bolzano&amp;#39;s Intermediate Value Theorem.</p>

<h2>Groups</h2><h3>Group 1: Natural Sciences and Mathematics</h3><p>24.10.2024 12:00 - 14:00, TAU Konetalo K2341D opetustila (40)<br>31.10.2024 12:00 - 14:00, TAU Konetalo K2341D opetustila (40)<br>07.11.2024 12:00 - 14:00, TAU Konetalo K2341D opetustila (40)<br>14.11.2024 12:00 - 14:00, TAU Konetalo K2341D opetustila (40)<br>21.11.2024 12:00 - 14:00, TAU Konetalo K2341D opetustila (40)<br>28.11.2024 12:00 - 14:00, TAU Konetalo K2341D opetustila (40)<br>05.12.2024 12:00 - 14:00, TAU Konetalo K2341D opetustila (40)<br></p><h2>Groups</h2><h3>Lecture Group 1: </h3><p>22.10.2024 14:00 - 16:00, TAU Tietotalo TC103 opetustila (30)<br>29.10.2024 14:00 - 16:00, TAU Tietotalo TC103 opetustila (30)<br>05.11.2024 14:00 - 16:00, TAU Tietotalo TC103 opetustila (30)<br>12.11.2024 14:00 - 16:00, TAU Tietotalo TC103 opetustila (30)<br>19.11.2024 14:00 - 16:00, TAU Tietotalo TC103 opetustila (30)<br>26.11.2024 14:00 - 16:00, TAU Tietotalo TC103 opetustila (30)<br>03.12.2024 14:00 - 16:00, TAU Tietotalo TC103 opetustila (30)<br></p><h2>Groups</h2><h3>Other Event: Math Shack (in English)</h3><p>25.10.2024 12:00 - 14:00, TAU Tietotalo TB223 Laskutupa (32)<br>28.10.2024 15:00 - 17:00, TAU Tietotalo TB223 Laskutupa (32)<br>01.11.2024 12:00 - 14:00, TAU Tietotalo TB223 Laskutupa (32)<br>04.11.2024 15:00 - 17:00, TAU Tietotalo TB223 Laskutupa (32)<br>08.11.2024 12:00 - 14:00, TAU Tietotalo TB223 Laskutupa (32)<br>11.11.2024 15:00 - 17:00, TAU Tietotalo TB223 Laskutupa (32)<br>15.11.2024 12:00 - 14:00, TAU Tietotalo TB223 Laskutupa (32)<br>18.11.2024 15:00 - 17:00, TAU Tietotalo TB223 Laskutupa (32)<br>22.11.2024 12:00 - 14:00, TAU Tietotalo TB223 Laskutupa (32)<br>25.11.2024 15:00 - 17:00, TAU Tietotalo TB223 Laskutupa (32)<br>29.11.2024 12:00 - 14:00, TAU Tietotalo TB223 Laskutupa (32)<br>02.12.2024 15:00 - 17:00, TAU Tietotalo TB223 Laskutupa (32)<br>06.12.2024 12:00 - 14:00, TAU Tietotalo TB223 Laskutupa (32)<br></p>

<p>This course introduces to the fundamentals of mathematical analysis at an adequate level of rigour. Upon successful completion of the course, a student will be able to</p><ul><li>determine the greatest lower bound and the least upper bound in simple cases,</li><li>study the convergence and the properties of sequences,</li><li>find limits and study continuity&#160;of functions,</li><li>use precise definitions to produce rigorous proofs of results that arise in this course using direct and indirect proof, induction and epsilon-delta technique,</li><li>deliver both oral and written presentations of her/his solutions.</li></ul>

Finnish

<h2>Prerequisites</h2><p>For the students of Bachelor&amp;#39;s Programme in Science and Engineering, no prerequisites are required.<br></p><h2>Recommended Prerequisites</h2><ul><li>Introduction to Analysis, MATH.MA.110, 5 cr</li><li>Introductory Calculus, MATH.APP.111, 5 cr</li></ul>

<p>Lebl, J., <i>Basic Analysis: Introduction to Real Analysis I</i></p><p>Thomson, B.S., Bruckner, J.B., Bruckner, A.M., <i>Elementary Real Analysis</i><br></p><p>Trench, W.F., <i>Introduction to Real Analysis</i></p>

Analysis A: Limit and Continuity, Small group teaching

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Analysis A: Limit and Continuity, 5 cr

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Analysis A: Limit and Continuity, Small group teaching